In the thesis we discuss binary hyperstructures of linear differential operators of the second order both in general and (inspired by models of specific time processes) in a special case of the Jacobi form. We also study binary hyperstructures constructed from distributive lattices and suggest transfer of this construction to n-ary hyperstructures. We use these hyperstructures to construct multiautomata and quasi-multiautomata. The input sets of all these automata structures are constructed so that the transfer of information for certain specific modeling time functions is facilitated. For this reason we use smooth positive functions or vectors components of which are real numbers or smooth positive functions. The above hyperstructures are state-sets of these automata structures. Finally, we investigate various types of compositions of the above multiautomata and quasi-multiautomata. In order to this we have to generalize the classical definitions of Dörfler. While some of the concepts can be transferred to the hyperstructure context rather easily, in the case of Cartesian composition the attempt to generalize it leads to some interesting results.

Responsive analytics are rapidly taking over the traditional data analytics dominated by the post-fact approaches in traditional data warehousing. Recent advancements in analytics demand placing analytical engines at the forefront of the system to react to updates occurring at high speed and detect patterns, trends and anomalies. These kinds of solutions find applications in Financial Systems, Industrial Control Systems, Business Intelligence and on-line Machine Learning among others. These applications are usually associated with Big Data and require the ability to react to constantly changing data in order to obtain timely insights and take proactive measures. Generally, these systems specify the analytical results or their basic elements in a query language, where the main task then is to maintain these results under frequent updates efficiently. The task of reacting to updates and analyzing changing data has been addressed in two ways in the literature: traditional business intelligence (BI) solutions focus on historical data analysis where the data is refreshed periodically and in batches, and stream processing solutions process streams of data from transient sources as flow (or set of flows) of data items. Both kinds of systems share the niche of reacting to updates (known as dynamic evaluation); however, they differ in architecture, query languages, and processing mechanisms. In this thesis, we investigate the possibility of a reactive and unified framework to model queries that appear in both kinds of systems. In traditional BI solutions, evaluating queries under updates has been studied under the umbrella of incremental evaluation of updates that is based on relational incremental view maintenance model and mostly focus on queries that feature equi-joins. Streaming systems, in contrast, generally follow the automaton based models to evaluate queries under updates, and they generally process queries that mostly feature comparisons of temporal attributes (e.g., timestamp attributes) along-with comparisons of non-temporal attributes over streams of bounded sizes. Temporal comparisons constitute inequality constraints, while non-temporal comparisons can either be equality or inequality constraints, hence these systems mostly process inequality joins. As starting point, we postulate the thesis that queries in streaming systems can also be evaluated efficiently based on the paradigm of incremental evaluation just like in BI systems in a main-memory model. The efficiency of such a model is measured in terms of runtime memory footprint and the update processing cost. To this end, the existing approaches of dynamic evaluation in both kind of systems present a trade-off between memory footprint and the update processing cost. More specifically, systems that avoid materialization of query (sub) results incur high update latency and systems that materialize (sub) results incur high memory footprint. We are interested in investigating the possibility to build a model that can address this trade-off. In particular, we overcome this trade-off by investigating the possibility of practical dynamic evaluation algorithm for queries that appear in both kinds of systems, and present a main-memory data representation that allows to enumerate query (sub) results without materialization and can be maintained efficiently under updates. We call this representation the Dynamic Constant Delay Linear Representation (DCLR). We devise DCLRs with the following properties: 1) they allow, without materialization, enumeration of query results with bounded-delay (and with constant delay for a sub-class of queries); 2) they allow tuple lookup in query results with logarithmic delay (and with constant delay for conjunctive queries with equi-joins only); 3) they take space linear in the size of the database; 4) they can be maintained efficiently under updates. We first study the DCLRs with the above-described properties for the class of acyclic conjunctive queries featuring equi-joins with projections and present the dynamic evaluation algorithm. Then, we present the generalization of thiw algorithm to the class of acyclic queries featuring multi-way theta-joins with projections. We devise DCLRs with the above properties for acyclic conjunctive queries, and the working of dynamic algorithms over DCLRs is based on a particular variant of join trees, called the Generalized Join Trees (GJTs) that guarantee the above-described properties of DCLRs. We define GJTs and present the algorithms to test a conjunctive query featuring theta-joins for acyclicity and to generate GJTs for such queries. To do this, we extend the classical GYO algorithm from testing a conjunctive query with equalities for acyclicity to test a conjunctive query featuring multi-way theta-joins with projections for acyclicity. We further extend the GYO algorithm to generate GJTs for queries that are acyclic. We implemented our algorithms in a query compiler that takes as input the SQL queries and generates Scala executable code – a trigger program to process queries and maintain under updates. We tested our approach against state of the art main-memory BI and CEP systems. Our evaluation results have shown that our DCLRs based approach is over an order of magnitude efficient than existing systems for both memory footprint and update processing cost. We have also shown that the enumeration of query results without materialization in DCLRs is comparable (and in some cases efficient) as compared to enumerating from materialized query results.

The main and fundamental goal of this work is the taxation of the various types of the companies. Of course, the height of taxation is one of the general questions. A lot of people are also interested in the way of guarantee. In the Czech law there are these types of companies: limited company, join stock company, special limited partnership and co partnership. In every company the economic result is to tax another system. The economic result is the difference between revenues and costs. But it cannot be considered a tax base. The economic result is increased by non-taxable costs. And this is called the tax base. In the Czech law there are two types of taxation. The first one is the legal entity income tax and its rate is 21 % and the other one is the natural person income and its rate is 15 % for both (in 2008).

<p>U radu je ispitan sledeći problem: <em>Pod kojim&nbsp;uslovima se može rekonstruisati&nbsp; (sintetisati)&nbsp;intervalno-vrednosni rasplinuti skup iz&nbsp; poznate&nbsp;familije nivo skupova.</em></p><p>U tu svrhu su proučena svojstva mreža&nbsp;intervala za svaki od četiri izabrana mrežna&nbsp;<br />uređenja: poredak po komponentama, neprecizni&nbsp;poredak (skupovna inkluzija), strogi &nbsp;i leksikografski&nbsp;poredak.&nbsp;</p><p>Definisane su i-između i ili-između ravne&nbsp;mreže&nbsp;&nbsp; i ispitana njihova svojstva potrebna za&nbsp;re&scaron;avanje postavljenog problema sinteze za&nbsp;intervalno-vrednosne rasplinute skupove. Za i-između ravne mreže je dokazano da su, u svom&nbsp;konačnom slučaju, slim mreže i dualno, da su ili-između ravne mreže dualno-slim mreže.</p><p>Data je karakterizacija kompletnih konačno&nbsp;prostornih i dualno konačno prostornih mreža.&nbsp;</p><p>Određena je klasa mreža koje se mogu&nbsp;injektivno preslikati u direktan proizvod n&nbsp;<br />kompletnih lanaca tako da su očuvani supremumi i&nbsp;dualno, određena je klasa mreža koje se mogu&nbsp;injektivno preslikati u direktan proizvod n lanaca&nbsp;tako da su očuvani infimumi.&nbsp;</p><p>U re&scaron;avanju problema sinteze posmatrana su&nbsp;dva tipa nivo skupova - gornji i donji nivo skupovi.&nbsp;Potreban i dovoljan uslov za sintezu intervalno-vrednosnog rasplinutog skupa iz poznate familije&nbsp;nivo skupova određen je za mrežu intervala koja je&nbsp;uređena poretkom po komponentama, za oba tipa&nbsp;posmatranih nivo skupova.</p><p>Za mrežu intervala uređenu nepreciznim&nbsp;poretkom, problem je re&scaron;en za donje nivo skupove,&nbsp;dok su za gornje nivo skupove određeni dovoljni&nbsp;uslovi.</p><p>Za mrežu intervala koja je uređena&nbsp;leksikografskim poretkom, takođe su dati dovoljni<br />uslovi i to za oba tipa nivo skupova.&nbsp;</p><p>Za mrežu intervala uređenu strogim poretkom&nbsp;problem nije re&scaron;avan, jer izlazi izvan okvira ovog&nbsp;rada.</p><p><br />Dobijeni rezultati su primenjeni za re&scaron;avanje&nbsp;sličnog problema sinteze za intervalno-vrednosne&nbsp;intuicionističke rasplinute skupove&nbsp; za mrežu&nbsp;intervala uređenu poretkom po komponentama.&nbsp;</p><p>Rezultati ovog istraživanja su od teorijskog&nbsp;značaja u teoriji mreža i teoriji rasplinutih skupova,&nbsp;ali postoji mogućnost za primenu u matematičkoj&nbsp;morfologiji i obradi slika.</p> / <p>In this thesis&nbsp; the following problem was investigated: Under which conditions an interval-valued fuzzy set can be reconstructed from the given family of cut sets.</p><p>We consider interval-valued fuzzy sets as&nbsp; a special type of lattice-valued fuzzy sets and&nbsp; we studied properties of lattices of intervals using four different lattice&nbsp; order: componentwise ordering, imprecision ordering (inclusion of sets), strong and&nbsp;lexicographical ordering.</p><p>We proposed new definitions&nbsp; of meet-between planar and join - between planar lattices, we investigated their properties and used them for solving problem of synthesis&nbsp; in&nbsp; interval-valued fuzzy sets.</p><p>It has been proven that finite meet- between planar lattices and slim lattices are equivalent, and dually:&nbsp;&nbsp;&nbsp; finite join-&nbsp; between planar lattices and dually slim lattices are equivalent.</p><p>Complete finitely&nbsp; spatial lattices and complete dually finitely spatial lattices are fully&nbsp;characterized&nbsp; in this setting. Next, we characterized&nbsp; lattices which can be order<br />embedded into a Cartesian product of&nbsp; n&nbsp; complete chains such that all suprema are preserved under the embedding.</p><p>And dually, we characterized lattices which can be order embedded into a Cartesian product of n complete chains such that all infima are preserved under the embedding.</p><p>We considered two types of cut sets &ndash; upper cuts and lower cuts.</p><p>Solution of the&nbsp; problem of synthesis of interval-valued fuzzy sets are given for lattices of intervals under componentwise ordering for both types of cut sets. Solution of problem of synthesis of&nbsp; interval-valued fuzzy sets&nbsp; are&nbsp; given for lower cuts for lattices of intervals under imprecision ordering.&nbsp; Sufficient conditions are given for lattices of intervals under imprecision ordering and family of upper cuts.</p><p>Sufficient conditions are also given for lattices of intervals under lexicographical ordering.</p><p>The problem of synthesis of interval-valued fuzzy sets for lattices of&nbsp; intervals under strong ordering is beyond the scope of this thesis.</p><p>A similar problem of synthesis of&nbsp; interval-valued intuitionistic fuzzy sets is solved for lattices of intervals under componentwise ordering.</p><p>These results are&nbsp; mostly of theoretical importance in lattice theory and fuzzy sets theory, but also they could&nbsp; be applied in mathematical morphology and in&nbsp; image processing.</p>